“Old” mobile phones used to save their SMS messages on a Simcard. With the right equipement data can be extracted out of these Simcards relatively easy.
A simple Simcard reader combined with software, provider by the NFI (Dutch Forensic Institute) Nederlands Forensich Instituut is all you need to get (deleted) data out of a Simcard.
The modern generation of phones hardly save data on Simcards anymore. More often this data is saved in the phone itself. The capacity of phones are growing and so are the possibility’s to retrieve deleted SMS Messages.
Sometimes thousands can be retrieved.

The times a mobile phone was only phone is way back. Phones have to be treated like computers to get the most out of it. This is truth for both visible data as for deleted messages. From mobile phones one can retrieve a wealth of information, if the phone is investigated in the right way.

Don’t forget applications like Ping, Whatsapp and iMessages. You will not find them on the simcard, but maybe you can find them on the phone.
If you don’t have the phone (anymore) but still have access to a computer the phone was synchronised with, we might be able to get date from the syntonisation-files.